A point object is recorded at from the plate using a collimated reference beam ( ) at

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Fourier optics and image formation · Fourier optics and image formation

What an Instrument Can See, Ch Keeping the phase: holography, wavefront modulation and adaptive optics

Problem

A point object is recorded at

z_o = 400\ \mathrm{mm}

from the plate using a collimated reference beam (

z_r \to \infty

) at

\lambda_1 = 488\ \mathrm{nm}

. The hologram is then optically copied at a linear magnification

m = 1.5

(the fringe pattern is enlarged by this factor). The enlarged copy is replayed by a point source at

z_p = 800\ \mathrm{mm}

and wavelength

\lambda_2 = 633\ \mathrm{nm}

. (a) Starting from the matching of quadratic and linear phases between the recording and replay fields, write down the general expressions for the image distance

z_i

and the lateral magnification

M

of the reconstructed point image in terms of

z_o, z_r, z_p, m, \lambda_1, \lambda_2

, and verify that both reduce to the expected

z_i = z_o

M=1

when

m=1

\lambda_1=\lambda_2

and

z_r, z_p\to\infty

. (b) Evaluate

z_i

and

M

for the stated numbers.

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